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AuthorKallenberg, Olav. author
TitleFoundations of Modern Probability [electronic resource] / by Olav Kallenberg
ImprintNew York, NY : Springer New York, 1997
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Descript XII, 523 p. online resource


From the reviews of the first edition: "... To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known material, such as Loeve's and more recently Rogers and Williams'. Seen in this light, Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands." Mathematical Reviews "... Indeed the monograph has the potential to become a (possibly even ̀̀the'') major reference book on large parts of probability theory for the next decade or more." Zentralblatt "The theory of probability has grown exponentially during the second half of the twentieth century and the idea of writing a single volume that could serve as a general reference for much of the modern theory seems almost foolhardy. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly. ... It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self- contained. ..." Metrica This new edition contains four new chapters as well as numerous improvements throughout the text


Elements of Measure Theory -- Processes, Distributions, and Independence -- Random Sequences, Series, and Averages -- Characteristic Functions and Classical Limit Theorems -- Conditioning and Disintegration -- Martingales and Optional Times -- Markov Processes and Discrete-Time Chains -- Random Walks and Renewal Theory -- Stationary Processes and Ergodic Theory -- Poisson and Pure Jump-Type Markov Processes -- Gaussian Processes and Brownian Motion -- Skorohod Embedding and Invariance Principles -- Independent Increments and Infinite Divisibility -- Convergence of Random Processes, Measures, and Sets -- Stochastic Integrals and Quadratic Variation -- Continuous Martingales and Brownian Motion -- Feller Processes and Semigroups -- Stochastic Differential Equations and Martingale Problems -- Local Time, Excursions, and Additive Functionals -- One-Dimensional SDEs and Diffusions -- PDE-Connections and Potential Theory -- Predictability, Compensation, and Excessive Functions -- Semimartingales and General Stochastic Integration

Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes


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